Can one remove the hadassim from the shoikilach on YomTov itself to put into water and then put them back again into the shoikelach? (Obviously this cannot be done when not using shoikelach because of tying and untying). Does this involve tikun kaili or any other concern?
There is no concern and it is permitted to take them out and put them into the koishiklech.
It is also permitted to put them in water (654:1), but the water should not be changed on Yom Tov.
Note that the koishiklech should be tied to the lulav (Mishnah Berurah 654:5).